Mathematical Sciences: Sklyanin Algebras & Graded Algebras

主要研究者Smith将研究有限表示的Notherian分次代数，特别是Sklyanin代数。对这些代数的研究在非对易代数几何的发展中具有重要意义。一个关键问题是对Sklyanin代数上的胖点模进行分类。这位首席研究者还将把他在四维Sklyanin代数上所得到的结果推广到高维。此外，还将研究Gelfand-Kirillov维为3的非交换曲面。这将使我们对非对易代数几何的大体有一个更清晰的理解。本研究属于非对易环论的一般领域。该项目中考虑的环在数学的许多领域都很有兴趣，包括代数几何。给定一条曲线，其中一个环可以与曲线上的某些点相关联。更好地理解这些环和这种联系将有助于确定给定曲线的几何形状。***

Smith The principal investigator will study finitely presented, noetherian graded algebras, particularly the Sklyanin algebras. The study of these algebras has been significant in the development of noncommutative algebraic geometry. A key problem is to classify the fat point modules over the Sklyanin algebras. The principal investigator will also extend to higher dimensions the results he has obtained on the 4-dimensional Sklyanin algebras. In addition, noncommutative surfaces of Gelfand-Kirillov dimension 3 will be studied. This will provide a clearer understanding of the general outline of noncommutative algebraic geometry. This research is in the general area of noncommutative ring theory. The rings considered in the project are of interest in many areas of mathematics including algebraic geometry. Given a curve, one of these rings can be associated with certain points on the curve. A better understanding of these rings and this association will be useful in determine the geometry of a given curve. ***